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arXiv · 2204.07750

Fusion systems realizing certain Todd modules

Bob Oliver
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Abstract

We study a certain family of simple fusion systems over finite $3$-groups, ones that involve Todd modules of the Mathieu groups $2M_{12}$, $M_{11}$, and $A_6=O^2(M_{10})$ over $\mathbb{F}_3$, and show that they are all isomorphic to the $3$-fusion systems of almost simple groups. As one consequence, we give new $3$-local characterizations of Conway's sporadic simple groups.

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Bob Oliver. 2022-04-16. Fusion systems realizing certain Todd modules. https://arxiv.org/abs/2204.07750

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